Loss vs. fee - breaking even

Market goes from 1:1 odds to 3:1 odds for YES (much more people bet on NO). Fee is 2%. How much turnover to break even? In the example below LP needs a turnover (stake from betters) to be ~22x initial liquidity to break even

Profit Loss heat map

Shows loss (more red) and profit (more green) made by LP as a function of total stake (how much was staked by betters) vs. odds divergence (how much betters shifted market from initial liquidity provision. example: LP thinks Trump:Biden is 1:1. better think that Trump:Biden is 3:1 and bet more against Trump)

summary of results below

  1. increasing liquidity does not change the break even
  2. LP has incentive to provide less liquidity to lower the impermanent loss. that of course increases the slippage which in turn decreases the volume. but if LP is event creator can raise volume in other ways and keep slippage high ie. 10%
  3. reinvesting fee as liquidity puts LP at more risk and break even comes later. on the other hand slippage decreases and that should boost volume. this will be hard to model as this is user behavior vs. slippage

TODO: if we increase fees then LP can risk more liquidity and we decrease slippage. model what is more efficient